TSTP Solution File: GRP669-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP669-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:44:49 EDT 2022
% Result : Unsatisfiable 0.51s 0.73s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 32
% Syntax : Number of clauses : 106 ( 58 unt; 0 nHn; 58 RR)
% Number of literals : 176 ( 175 equ; 73 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 257 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c03,axiom,
mult(rd(A,B),B) = A ).
cnf(c04,axiom,
rd(mult(A,B),B) = A ).
cnf(c05,axiom,
mult(A,unit) = A ).
cnf(c07,axiom,
mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) ).
cnf(c08,axiom,
mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) ).
cnf(c10,axiom,
mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) ).
cnf(goals,negated_conjecture,
mult(mult(a,b),mult(c,mult(a,b))) != mult(mult(mult(a,mult(b,c)),a),b) ).
cnf(refute_0_0,plain,
mult(mult(b,c),mult(a,b)) = mult(b,mult(mult(c,a),b)),
inference(subst,[],[c10:[bind(A,$fot(b)),bind(B,$fot(c)),bind(C,$fot(a))]]) ).
cnf(refute_0_1,plain,
mult(a,mult(mult(b,c),mult(a,b))) = mult(a,mult(mult(b,c),mult(a,b))),
introduced(tautology,[refl,[$fot(mult(a,mult(mult(b,c),mult(a,b))))]]) ).
cnf(refute_0_2,plain,
( mult(a,mult(mult(b,c),mult(a,b))) != mult(a,mult(mult(b,c),mult(a,b)))
| mult(mult(b,c),mult(a,b)) != mult(b,mult(mult(c,a),b))
| mult(a,mult(mult(b,c),mult(a,b))) = mult(a,mult(b,mult(mult(c,a),b))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(a,mult(mult(b,c),mult(a,b))),mult(a,mult(mult(b,c),mult(a,b)))) ),[1,1],$fot(mult(b,mult(mult(c,a),b)))]]) ).
cnf(refute_0_3,plain,
( mult(mult(b,c),mult(a,b)) != mult(b,mult(mult(c,a),b))
| mult(a,mult(mult(b,c),mult(a,b))) = mult(a,mult(b,mult(mult(c,a),b))) ),
inference(resolve,[$cnf( $equal(mult(a,mult(mult(b,c),mult(a,b))),mult(a,mult(mult(b,c),mult(a,b)))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
mult(a,mult(mult(b,c),mult(a,b))) = mult(a,mult(b,mult(mult(c,a),b))),
inference(resolve,[$cnf( $equal(mult(mult(b,c),mult(a,b)),mult(b,mult(mult(c,a),b))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_6,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_7,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( mult(A,mult(B,mult(A,C))) != mult(mult(mult(A,B),A),C)
| mult(mult(mult(A,B),A),C) = mult(A,mult(B,mult(A,C))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(mult(A,mult(B,mult(A,C))))),bind(Y,$fot(mult(mult(mult(A,B),A),C)))]]) ).
cnf(refute_0_9,plain,
mult(mult(mult(A,B),A),C) = mult(A,mult(B,mult(A,C))),
inference(resolve,[$cnf( $equal(mult(A,mult(B,mult(A,C))),mult(mult(mult(A,B),A),C)) )],[c07,refute_0_8]) ).
cnf(refute_0_10,plain,
mult(mult(mult(a,mult(b,c)),a),b) = mult(a,mult(mult(b,c),mult(a,b))),
inference(subst,[],[refute_0_9:[bind(A,$fot(a)),bind(B,$fot(mult(b,c))),bind(C,$fot(b))]]) ).
cnf(refute_0_11,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_12,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
( mult(a,mult(mult(b,c),mult(a,b))) != mult(a,mult(b,mult(mult(c,a),b)))
| mult(mult(mult(a,mult(b,c)),a),b) != mult(a,mult(mult(b,c),mult(a,b)))
| mult(mult(mult(a,mult(b,c)),a),b) = mult(a,mult(b,mult(mult(c,a),b))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(mult(mult(mult(a,mult(b,c)),a),b))),bind(Y,$fot(mult(a,mult(mult(b,c),mult(a,b))))),bind(Z,$fot(mult(a,mult(b,mult(mult(c,a),b)))))]]) ).
cnf(refute_0_14,plain,
( mult(a,mult(mult(b,c),mult(a,b))) != mult(a,mult(b,mult(mult(c,a),b)))
| mult(mult(mult(a,mult(b,c)),a),b) = mult(a,mult(b,mult(mult(c,a),b))) ),
inference(resolve,[$cnf( $equal(mult(mult(mult(a,mult(b,c)),a),b),mult(a,mult(mult(b,c),mult(a,b)))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
mult(mult(mult(a,mult(b,c)),a),b) = mult(a,mult(b,mult(mult(c,a),b))),
inference(resolve,[$cnf( $equal(mult(a,mult(mult(b,c),mult(a,b))),mult(a,mult(b,mult(mult(c,a),b)))) )],[refute_0_4,refute_0_14]) ).
cnf(refute_0_16,plain,
( mult(mult(a,b),mult(c,mult(a,b))) != mult(a,mult(b,mult(mult(c,a),b)))
| mult(mult(mult(a,mult(b,c)),a),b) != mult(a,mult(b,mult(mult(c,a),b)))
| mult(mult(a,b),mult(c,mult(a,b))) = mult(mult(mult(a,mult(b,c)),a),b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(mult(a,b),mult(c,mult(a,b))),mult(mult(mult(a,mult(b,c)),a),b)) ),[1],$fot(mult(a,mult(b,mult(mult(c,a),b))))]]) ).
cnf(refute_0_17,plain,
( mult(mult(a,b),mult(c,mult(a,b))) != mult(a,mult(b,mult(mult(c,a),b)))
| mult(mult(a,b),mult(c,mult(a,b))) = mult(mult(mult(a,mult(b,c)),a),b) ),
inference(resolve,[$cnf( $equal(mult(mult(mult(a,mult(b,c)),a),b),mult(a,mult(b,mult(mult(c,a),b)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
mult(mult(a,b),mult(c,mult(a,b))) != mult(a,mult(b,mult(mult(c,a),b))),
inference(resolve,[$cnf( $equal(mult(mult(a,b),mult(c,mult(a,b))),mult(mult(mult(a,mult(b,c)),a),b)) )],[refute_0_17,goals]) ).
cnf(refute_0_19,plain,
rd(mult(mult(mult(X_18,X_19),X_18),B),B) = mult(mult(X_18,X_19),X_18),
inference(subst,[],[c04:[bind(A,$fot(mult(mult(X_18,X_19),X_18)))]]) ).
cnf(refute_0_20,plain,
mult(X_18,mult(X_19,mult(X_18,B))) = mult(mult(mult(X_18,X_19),X_18),B),
inference(subst,[],[c07:[bind(A,$fot(X_18)),bind(B,$fot(X_19)),bind(C,$fot(B))]]) ).
cnf(refute_0_21,plain,
( mult(X_18,mult(X_19,mult(X_18,B))) != mult(mult(mult(X_18,X_19),X_18),B)
| mult(mult(mult(X_18,X_19),X_18),B) = mult(X_18,mult(X_19,mult(X_18,B))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(mult(X_18,mult(X_19,mult(X_18,B))))),bind(Y,$fot(mult(mult(mult(X_18,X_19),X_18),B)))]]) ).
cnf(refute_0_22,plain,
mult(mult(mult(X_18,X_19),X_18),B) = mult(X_18,mult(X_19,mult(X_18,B))),
inference(resolve,[$cnf( $equal(mult(X_18,mult(X_19,mult(X_18,B))),mult(mult(mult(X_18,X_19),X_18),B)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( mult(mult(mult(X_18,X_19),X_18),B) != mult(X_18,mult(X_19,mult(X_18,B)))
| rd(mult(mult(mult(X_18,X_19),X_18),B),B) != mult(mult(X_18,X_19),X_18)
| rd(mult(X_18,mult(X_19,mult(X_18,B))),B) = mult(mult(X_18,X_19),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(mult(mult(X_18,X_19),X_18),B),B),mult(mult(X_18,X_19),X_18)) ),[0,0],$fot(mult(X_18,mult(X_19,mult(X_18,B))))]]) ).
cnf(refute_0_24,plain,
( rd(mult(mult(mult(X_18,X_19),X_18),B),B) != mult(mult(X_18,X_19),X_18)
| rd(mult(X_18,mult(X_19,mult(X_18,B))),B) = mult(mult(X_18,X_19),X_18) ),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_18,X_19),X_18),B),mult(X_18,mult(X_19,mult(X_18,B)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
rd(mult(X_18,mult(X_19,mult(X_18,B))),B) = mult(mult(X_18,X_19),X_18),
inference(resolve,[$cnf( $equal(rd(mult(mult(mult(X_18,X_19),X_18),B),B),mult(mult(X_18,X_19),X_18)) )],[refute_0_19,refute_0_24]) ).
cnf(refute_0_26,plain,
mult(mult(mult(X_18,X_19),X_18),unit) = mult(mult(X_18,X_19),X_18),
inference(subst,[],[c05:[bind(A,$fot(mult(mult(X_18,X_19),X_18)))]]) ).
cnf(refute_0_27,plain,
mult(X_18,mult(X_19,mult(X_18,unit))) = mult(mult(mult(X_18,X_19),X_18),unit),
inference(subst,[],[c07:[bind(A,$fot(X_18)),bind(B,$fot(X_19)),bind(C,$fot(unit))]]) ).
cnf(refute_0_28,plain,
( mult(X_18,mult(X_19,mult(X_18,unit))) != mult(mult(mult(X_18,X_19),X_18),unit)
| mult(mult(mult(X_18,X_19),X_18),unit) = mult(X_18,mult(X_19,mult(X_18,unit))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(mult(X_18,mult(X_19,mult(X_18,unit))))),bind(Y,$fot(mult(mult(mult(X_18,X_19),X_18),unit)))]]) ).
cnf(refute_0_29,plain,
mult(mult(mult(X_18,X_19),X_18),unit) = mult(X_18,mult(X_19,mult(X_18,unit))),
inference(resolve,[$cnf( $equal(mult(X_18,mult(X_19,mult(X_18,unit))),mult(mult(mult(X_18,X_19),X_18),unit)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( mult(mult(mult(X_18,X_19),X_18),unit) != mult(X_18,mult(X_19,mult(X_18,unit)))
| mult(mult(mult(X_18,X_19),X_18),unit) != mult(mult(X_18,X_19),X_18)
| mult(X_18,mult(X_19,mult(X_18,unit))) = mult(mult(X_18,X_19),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(mult(X_18,X_19),X_18),unit),mult(mult(X_18,X_19),X_18)) ),[0],$fot(mult(X_18,mult(X_19,mult(X_18,unit))))]]) ).
cnf(refute_0_31,plain,
( mult(mult(mult(X_18,X_19),X_18),unit) != mult(mult(X_18,X_19),X_18)
| mult(X_18,mult(X_19,mult(X_18,unit))) = mult(mult(X_18,X_19),X_18) ),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_18,X_19),X_18),unit),mult(X_18,mult(X_19,mult(X_18,unit)))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
mult(X_18,mult(X_19,mult(X_18,unit))) = mult(mult(X_18,X_19),X_18),
inference(resolve,[$cnf( $equal(mult(mult(mult(X_18,X_19),X_18),unit),mult(mult(X_18,X_19),X_18)) )],[refute_0_26,refute_0_31]) ).
cnf(refute_0_33,plain,
mult(X_18,unit) = X_18,
inference(subst,[],[c05:[bind(A,$fot(X_18))]]) ).
cnf(refute_0_34,plain,
mult(X_19,mult(X_18,unit)) = mult(X_19,mult(X_18,unit)),
introduced(tautology,[refl,[$fot(mult(X_19,mult(X_18,unit)))]]) ).
cnf(refute_0_35,plain,
( mult(X_18,unit) != X_18
| mult(X_19,mult(X_18,unit)) != mult(X_19,mult(X_18,unit))
| mult(X_19,mult(X_18,unit)) = mult(X_19,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_19,mult(X_18,unit)),mult(X_19,mult(X_18,unit))) ),[1,1],$fot(X_18)]]) ).
cnf(refute_0_36,plain,
( mult(X_18,unit) != X_18
| mult(X_19,mult(X_18,unit)) = mult(X_19,X_18) ),
inference(resolve,[$cnf( $equal(mult(X_19,mult(X_18,unit)),mult(X_19,mult(X_18,unit))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
mult(X_19,mult(X_18,unit)) = mult(X_19,X_18),
inference(resolve,[$cnf( $equal(mult(X_18,unit),X_18) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
mult(X_18,mult(X_19,mult(X_18,unit))) = mult(X_18,mult(X_19,mult(X_18,unit))),
introduced(tautology,[refl,[$fot(mult(X_18,mult(X_19,mult(X_18,unit))))]]) ).
cnf(refute_0_39,plain,
( mult(X_18,mult(X_19,mult(X_18,unit))) != mult(X_18,mult(X_19,mult(X_18,unit)))
| mult(X_19,mult(X_18,unit)) != mult(X_19,X_18)
| mult(X_18,mult(X_19,mult(X_18,unit))) = mult(X_18,mult(X_19,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_18,mult(X_19,mult(X_18,unit))),mult(X_18,mult(X_19,mult(X_18,unit)))) ),[1,1],$fot(mult(X_19,X_18))]]) ).
cnf(refute_0_40,plain,
( mult(X_19,mult(X_18,unit)) != mult(X_19,X_18)
| mult(X_18,mult(X_19,mult(X_18,unit))) = mult(X_18,mult(X_19,X_18)) ),
inference(resolve,[$cnf( $equal(mult(X_18,mult(X_19,mult(X_18,unit))),mult(X_18,mult(X_19,mult(X_18,unit)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
mult(X_18,mult(X_19,mult(X_18,unit))) = mult(X_18,mult(X_19,X_18)),
inference(resolve,[$cnf( $equal(mult(X_19,mult(X_18,unit)),mult(X_19,X_18)) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
( mult(X_18,mult(X_19,mult(X_18,unit))) != mult(X_18,mult(X_19,X_18))
| mult(X_18,mult(X_19,mult(X_18,unit))) != mult(mult(X_18,X_19),X_18)
| mult(X_18,mult(X_19,X_18)) = mult(mult(X_18,X_19),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_18,mult(X_19,mult(X_18,unit))),mult(mult(X_18,X_19),X_18)) ),[0],$fot(mult(X_18,mult(X_19,X_18)))]]) ).
cnf(refute_0_43,plain,
( mult(X_18,mult(X_19,mult(X_18,unit))) != mult(mult(X_18,X_19),X_18)
| mult(X_18,mult(X_19,X_18)) = mult(mult(X_18,X_19),X_18) ),
inference(resolve,[$cnf( $equal(mult(X_18,mult(X_19,mult(X_18,unit))),mult(X_18,mult(X_19,X_18))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
mult(X_18,mult(X_19,X_18)) = mult(mult(X_18,X_19),X_18),
inference(resolve,[$cnf( $equal(mult(X_18,mult(X_19,mult(X_18,unit))),mult(mult(X_18,X_19),X_18)) )],[refute_0_32,refute_0_43]) ).
cnf(refute_0_45,plain,
( mult(X_18,mult(X_19,X_18)) != mult(mult(X_18,X_19),X_18)
| mult(mult(X_18,X_19),X_18) = mult(X_18,mult(X_19,X_18)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(mult(X_18,mult(X_19,X_18)))),bind(Y,$fot(mult(mult(X_18,X_19),X_18)))]]) ).
cnf(refute_0_46,plain,
mult(mult(X_18,X_19),X_18) = mult(X_18,mult(X_19,X_18)),
inference(resolve,[$cnf( $equal(mult(X_18,mult(X_19,X_18)),mult(mult(X_18,X_19),X_18)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( mult(mult(X_18,X_19),X_18) != mult(X_18,mult(X_19,X_18))
| rd(mult(X_18,mult(X_19,mult(X_18,B))),B) != mult(mult(X_18,X_19),X_18)
| rd(mult(X_18,mult(X_19,mult(X_18,B))),B) = mult(X_18,mult(X_19,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(X_18,mult(X_19,mult(X_18,B))),B),mult(mult(X_18,X_19),X_18)) ),[1],$fot(mult(X_18,mult(X_19,X_18)))]]) ).
cnf(refute_0_48,plain,
( rd(mult(X_18,mult(X_19,mult(X_18,B))),B) != mult(mult(X_18,X_19),X_18)
| rd(mult(X_18,mult(X_19,mult(X_18,B))),B) = mult(X_18,mult(X_19,X_18)) ),
inference(resolve,[$cnf( $equal(mult(mult(X_18,X_19),X_18),mult(X_18,mult(X_19,X_18))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
rd(mult(X_18,mult(X_19,mult(X_18,B))),B) = mult(X_18,mult(X_19,X_18)),
inference(resolve,[$cnf( $equal(rd(mult(X_18,mult(X_19,mult(X_18,B))),B),mult(mult(X_18,X_19),X_18)) )],[refute_0_25,refute_0_48]) ).
cnf(refute_0_50,plain,
rd(mult(mult(A,B),mult(X_103,mult(mult(A,B),mult(C,A)))),mult(C,A)) = mult(mult(A,B),mult(X_103,mult(A,B))),
inference(subst,[],[refute_0_49:[bind(B,$fot(mult(C,A))),bind(X_18,$fot(mult(A,B))),bind(X_19,$fot(X_103))]]) ).
cnf(refute_0_51,plain,
( mult(mult(A,B),mult(C,A)) != mult(A,mult(mult(B,C),A))
| rd(mult(mult(A,B),mult(X_103,mult(mult(A,B),mult(C,A)))),mult(C,A)) != mult(mult(A,B),mult(X_103,mult(A,B)))
| rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)) = mult(mult(A,B),mult(X_103,mult(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(mult(A,B),mult(X_103,mult(mult(A,B),mult(C,A)))),mult(C,A)),mult(mult(A,B),mult(X_103,mult(A,B)))) ),[0,0,1,1],$fot(mult(A,mult(mult(B,C),A)))]]) ).
cnf(refute_0_52,plain,
( rd(mult(mult(A,B),mult(X_103,mult(mult(A,B),mult(C,A)))),mult(C,A)) != mult(mult(A,B),mult(X_103,mult(A,B)))
| rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)) = mult(mult(A,B),mult(X_103,mult(A,B))) ),
inference(resolve,[$cnf( $equal(mult(mult(A,B),mult(C,A)),mult(A,mult(mult(B,C),A))) )],[c10,refute_0_51]) ).
cnf(refute_0_53,plain,
rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)) = mult(mult(A,B),mult(X_103,mult(A,B))),
inference(resolve,[$cnf( $equal(rd(mult(mult(A,B),mult(X_103,mult(mult(A,B),mult(C,A)))),mult(C,A)),mult(mult(A,B),mult(X_103,mult(A,B)))) )],[refute_0_50,refute_0_52]) ).
cnf(refute_0_54,plain,
rd(mult(B,mult(mult(X_103,A),mult(B,C))),C) = mult(B,mult(mult(X_103,A),B)),
inference(subst,[],[refute_0_49:[bind(B,$fot(C)),bind(X_18,$fot(B)),bind(X_19,$fot(mult(X_103,A)))]]) ).
cnf(refute_0_55,plain,
mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C)) = mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C)),
introduced(tautology,[refl,[$fot(mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C)))]]) ).
cnf(refute_0_56,plain,
( mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C)) != mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C))
| rd(mult(B,mult(mult(X_103,A),mult(B,C))),C) != mult(B,mult(mult(X_103,A),B))
| mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C)) = mult(A,mult(B,mult(mult(X_103,A),B))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C)),mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C))) ),[1,1],$fot(mult(B,mult(mult(X_103,A),B)))]]) ).
cnf(refute_0_57,plain,
( rd(mult(B,mult(mult(X_103,A),mult(B,C))),C) != mult(B,mult(mult(X_103,A),B))
| mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C)) = mult(A,mult(B,mult(mult(X_103,A),B))) ),
inference(resolve,[$cnf( $equal(mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C)),mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C)) = mult(A,mult(B,mult(mult(X_103,A),B))),
inference(resolve,[$cnf( $equal(rd(mult(B,mult(mult(X_103,A),mult(B,C))),C),mult(B,mult(mult(X_103,A),B))) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
rd(mult(mult(X_38,X_39),mult(X_40,X_38)),mult(X_40,X_38)) = mult(X_38,X_39),
inference(subst,[],[c04:[bind(A,$fot(mult(X_38,X_39))),bind(B,$fot(mult(X_40,X_38)))]]) ).
cnf(refute_0_60,plain,
mult(mult(X_38,X_39),mult(X_40,X_38)) = mult(X_38,mult(mult(X_39,X_40),X_38)),
inference(subst,[],[c10:[bind(A,$fot(X_38)),bind(B,$fot(X_39)),bind(C,$fot(X_40))]]) ).
cnf(refute_0_61,plain,
( mult(mult(X_38,X_39),mult(X_40,X_38)) != mult(X_38,mult(mult(X_39,X_40),X_38))
| rd(mult(mult(X_38,X_39),mult(X_40,X_38)),mult(X_40,X_38)) != mult(X_38,X_39)
| rd(mult(X_38,mult(mult(X_39,X_40),X_38)),mult(X_40,X_38)) = mult(X_38,X_39) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(mult(X_38,X_39),mult(X_40,X_38)),mult(X_40,X_38)),mult(X_38,X_39)) ),[0,0],$fot(mult(X_38,mult(mult(X_39,X_40),X_38)))]]) ).
cnf(refute_0_62,plain,
( rd(mult(mult(X_38,X_39),mult(X_40,X_38)),mult(X_40,X_38)) != mult(X_38,X_39)
| rd(mult(X_38,mult(mult(X_39,X_40),X_38)),mult(X_40,X_38)) = mult(X_38,X_39) ),
inference(resolve,[$cnf( $equal(mult(mult(X_38,X_39),mult(X_40,X_38)),mult(X_38,mult(mult(X_39,X_40),X_38))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
rd(mult(X_38,mult(mult(X_39,X_40),X_38)),mult(X_40,X_38)) = mult(X_38,X_39),
inference(resolve,[$cnf( $equal(rd(mult(mult(X_38,X_39),mult(X_40,X_38)),mult(X_40,X_38)),mult(X_38,X_39)) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
rd(mult(X_78,mult(mult(rd(A,X_80),X_80),X_78)),mult(X_80,X_78)) = mult(X_78,rd(A,X_80)),
inference(subst,[],[refute_0_63:[bind(X_38,$fot(X_78)),bind(X_39,$fot(rd(A,X_80))),bind(X_40,$fot(X_80))]]) ).
cnf(refute_0_65,plain,
mult(rd(A,X_80),X_80) = A,
inference(subst,[],[c03:[bind(B,$fot(X_80))]]) ).
cnf(refute_0_66,plain,
( mult(rd(A,X_80),X_80) != A
| rd(mult(X_78,mult(mult(rd(A,X_80),X_80),X_78)),mult(X_80,X_78)) != mult(X_78,rd(A,X_80))
| rd(mult(X_78,mult(A,X_78)),mult(X_80,X_78)) = mult(X_78,rd(A,X_80)) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(X_78,mult(mult(rd(A,X_80),X_80),X_78)),mult(X_80,X_78)),mult(X_78,rd(A,X_80))) ),[0,0,1,0],$fot(A)]]) ).
cnf(refute_0_67,plain,
( rd(mult(X_78,mult(mult(rd(A,X_80),X_80),X_78)),mult(X_80,X_78)) != mult(X_78,rd(A,X_80))
| rd(mult(X_78,mult(A,X_78)),mult(X_80,X_78)) = mult(X_78,rd(A,X_80)) ),
inference(resolve,[$cnf( $equal(mult(rd(A,X_80),X_80),A) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
rd(mult(X_78,mult(A,X_78)),mult(X_80,X_78)) = mult(X_78,rd(A,X_80)),
inference(resolve,[$cnf( $equal(rd(mult(X_78,mult(mult(rd(A,X_80),X_80),X_78)),mult(X_80,X_78)),mult(X_78,rd(A,X_80))) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
rd(mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)),mult(C,A)) = mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C)),
inference(subst,[],[refute_0_68:[bind(A,$fot(mult(B,mult(mult(X_103,A),mult(B,C))))),bind(X_78,$fot(A)),bind(X_80,$fot(C))]]) ).
cnf(refute_0_70,plain,
( mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C)) != mult(A,mult(B,mult(mult(X_103,A),B)))
| rd(mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)),mult(C,A)) != mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C))
| rd(mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)),mult(C,A)) = mult(A,mult(B,mult(mult(X_103,A),B))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(rd(mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)),mult(C,A)))),bind(Y,$fot(mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C)))),bind(Z,$fot(mult(A,mult(B,mult(mult(X_103,A),B)))))]]) ).
cnf(refute_0_71,plain,
( mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C)) != mult(A,mult(B,mult(mult(X_103,A),B)))
| rd(mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)),mult(C,A)) = mult(A,mult(B,mult(mult(X_103,A),B))) ),
inference(resolve,[$cnf( $equal(rd(mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)),mult(C,A)),mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
rd(mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)),mult(C,A)) = mult(A,mult(B,mult(mult(X_103,A),B))),
inference(resolve,[$cnf( $equal(mult(A,rd(mult(B,mult(mult(X_103,A),mult(B,C))),C)),mult(A,mult(B,mult(mult(X_103,A),B)))) )],[refute_0_58,refute_0_71]) ).
cnf(refute_0_73,plain,
mult(mult(X_38,X_39),mult(mult(mult(A,X_38),C),X_38)) = mult(X_38,mult(mult(X_39,mult(mult(A,X_38),C)),X_38)),
inference(subst,[],[c10:[bind(A,$fot(X_38)),bind(B,$fot(X_39)),bind(C,$fot(mult(mult(A,X_38),C)))]]) ).
cnf(refute_0_74,plain,
mult(A,mult(X_38,mult(C,X_38))) = mult(mult(mult(A,X_38),C),X_38),
inference(subst,[],[c08:[bind(B,$fot(X_38))]]) ).
cnf(refute_0_75,plain,
( mult(A,mult(X_38,mult(C,X_38))) != mult(mult(mult(A,X_38),C),X_38)
| mult(mult(mult(A,X_38),C),X_38) = mult(A,mult(X_38,mult(C,X_38))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(mult(A,mult(X_38,mult(C,X_38))))),bind(Y,$fot(mult(mult(mult(A,X_38),C),X_38)))]]) ).
cnf(refute_0_76,plain,
mult(mult(mult(A,X_38),C),X_38) = mult(A,mult(X_38,mult(C,X_38))),
inference(resolve,[$cnf( $equal(mult(A,mult(X_38,mult(C,X_38))),mult(mult(mult(A,X_38),C),X_38)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( mult(mult(X_38,X_39),mult(mult(mult(A,X_38),C),X_38)) != mult(X_38,mult(mult(X_39,mult(mult(A,X_38),C)),X_38))
| mult(mult(mult(A,X_38),C),X_38) != mult(A,mult(X_38,mult(C,X_38)))
| mult(mult(X_38,X_39),mult(A,mult(X_38,mult(C,X_38)))) = mult(X_38,mult(mult(X_39,mult(mult(A,X_38),C)),X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_38,X_39),mult(mult(mult(A,X_38),C),X_38)),mult(X_38,mult(mult(X_39,mult(mult(A,X_38),C)),X_38))) ),[0,1],$fot(mult(A,mult(X_38,mult(C,X_38))))]]) ).
cnf(refute_0_78,plain,
( mult(mult(X_38,X_39),mult(mult(mult(A,X_38),C),X_38)) != mult(X_38,mult(mult(X_39,mult(mult(A,X_38),C)),X_38))
| mult(mult(X_38,X_39),mult(A,mult(X_38,mult(C,X_38)))) = mult(X_38,mult(mult(X_39,mult(mult(A,X_38),C)),X_38)) ),
inference(resolve,[$cnf( $equal(mult(mult(mult(A,X_38),C),X_38),mult(A,mult(X_38,mult(C,X_38)))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
mult(mult(X_38,X_39),mult(A,mult(X_38,mult(C,X_38)))) = mult(X_38,mult(mult(X_39,mult(mult(A,X_38),C)),X_38)),
inference(resolve,[$cnf( $equal(mult(mult(X_38,X_39),mult(mult(mult(A,X_38),C),X_38)),mult(X_38,mult(mult(X_39,mult(mult(A,X_38),C)),X_38))) )],[refute_0_73,refute_0_78]) ).
cnf(refute_0_80,plain,
mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))) = mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)),
inference(subst,[],[refute_0_79:[bind(A,$fot(X_103)),bind(C,$fot(mult(B,C))),bind(X_38,$fot(A)),bind(X_39,$fot(B))]]) ).
cnf(refute_0_81,plain,
rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)) = rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)),
introduced(tautology,[refl,[$fot(rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)))]]) ).
cnf(refute_0_82,plain,
( mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))) != mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A))
| rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)) != rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A))
| rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)) = rd(mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)),mult(C,A)) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)),rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A))) ),[1,0],$fot(mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)))]]) ).
cnf(refute_0_83,plain,
( mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))) != mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A))
| rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)) = rd(mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)),mult(C,A)) ),
inference(resolve,[$cnf( $equal(rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)),rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)) = rd(mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)),mult(C,A)),
inference(resolve,[$cnf( $equal(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A))) )],[refute_0_80,refute_0_83]) ).
cnf(refute_0_85,plain,
( rd(mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)),mult(C,A)) != mult(A,mult(B,mult(mult(X_103,A),B)))
| rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)) != rd(mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)),mult(C,A))
| rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)) = mult(A,mult(B,mult(mult(X_103,A),B))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)))),bind(Y,$fot(rd(mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)),mult(C,A)))),bind(Z,$fot(mult(A,mult(B,mult(mult(X_103,A),B)))))]]) ).
cnf(refute_0_86,plain,
( rd(mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)),mult(C,A)) != mult(A,mult(B,mult(mult(X_103,A),B)))
| rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)) = mult(A,mult(B,mult(mult(X_103,A),B))) ),
inference(resolve,[$cnf( $equal(rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)),rd(mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)),mult(C,A))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)) = mult(A,mult(B,mult(mult(X_103,A),B))),
inference(resolve,[$cnf( $equal(rd(mult(A,mult(mult(B,mult(mult(X_103,A),mult(B,C))),A)),mult(C,A)),mult(A,mult(B,mult(mult(X_103,A),B)))) )],[refute_0_72,refute_0_86]) ).
cnf(refute_0_88,plain,
( rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)) != mult(A,mult(B,mult(mult(X_103,A),B)))
| rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)) != mult(mult(A,B),mult(X_103,mult(A,B)))
| mult(A,mult(B,mult(mult(X_103,A),B))) = mult(mult(A,B),mult(X_103,mult(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)),mult(mult(A,B),mult(X_103,mult(A,B)))) ),[0],$fot(mult(A,mult(B,mult(mult(X_103,A),B))))]]) ).
cnf(refute_0_89,plain,
( rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)) != mult(mult(A,B),mult(X_103,mult(A,B)))
| mult(A,mult(B,mult(mult(X_103,A),B))) = mult(mult(A,B),mult(X_103,mult(A,B))) ),
inference(resolve,[$cnf( $equal(rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)),mult(A,mult(B,mult(mult(X_103,A),B)))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
mult(A,mult(B,mult(mult(X_103,A),B))) = mult(mult(A,B),mult(X_103,mult(A,B))),
inference(resolve,[$cnf( $equal(rd(mult(mult(A,B),mult(X_103,mult(A,mult(mult(B,C),A)))),mult(C,A)),mult(mult(A,B),mult(X_103,mult(A,B)))) )],[refute_0_53,refute_0_89]) ).
cnf(refute_0_91,plain,
( mult(A,mult(B,mult(mult(X_103,A),B))) != mult(mult(A,B),mult(X_103,mult(A,B)))
| mult(mult(A,B),mult(X_103,mult(A,B))) = mult(A,mult(B,mult(mult(X_103,A),B))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(mult(A,mult(B,mult(mult(X_103,A),B))))),bind(Y,$fot(mult(mult(A,B),mult(X_103,mult(A,B)))))]]) ).
cnf(refute_0_92,plain,
mult(mult(A,B),mult(X_103,mult(A,B))) = mult(A,mult(B,mult(mult(X_103,A),B))),
inference(resolve,[$cnf( $equal(mult(A,mult(B,mult(mult(X_103,A),B))),mult(mult(A,B),mult(X_103,mult(A,B)))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
mult(mult(a,b),mult(c,mult(a,b))) = mult(a,mult(b,mult(mult(c,a),b))),
inference(subst,[],[refute_0_92:[bind(A,$fot(a)),bind(B,$fot(b)),bind(X_103,$fot(c))]]) ).
cnf(refute_0_94,plain,
( mult(a,mult(b,mult(mult(c,a),b))) != mult(a,mult(b,mult(mult(c,a),b)))
| mult(mult(a,b),mult(c,mult(a,b))) != mult(a,mult(b,mult(mult(c,a),b)))
| mult(mult(a,b),mult(c,mult(a,b))) = mult(a,mult(b,mult(mult(c,a),b))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(a,b),mult(c,mult(a,b))),mult(a,mult(b,mult(mult(c,a),b)))) ),[1],$fot(mult(a,mult(b,mult(mult(c,a),b))))]]) ).
cnf(refute_0_95,plain,
( mult(a,mult(b,mult(mult(c,a),b))) != mult(a,mult(b,mult(mult(c,a),b)))
| mult(mult(a,b),mult(c,mult(a,b))) = mult(a,mult(b,mult(mult(c,a),b))) ),
inference(resolve,[$cnf( $equal(mult(mult(a,b),mult(c,mult(a,b))),mult(a,mult(b,mult(mult(c,a),b)))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
mult(a,mult(b,mult(mult(c,a),b))) != mult(a,mult(b,mult(mult(c,a),b))),
inference(resolve,[$cnf( $equal(mult(mult(a,b),mult(c,mult(a,b))),mult(a,mult(b,mult(mult(c,a),b)))) )],[refute_0_95,refute_0_18]) ).
cnf(refute_0_97,plain,
mult(a,mult(b,mult(mult(c,a),b))) = mult(a,mult(b,mult(mult(c,a),b))),
introduced(tautology,[refl,[$fot(mult(a,mult(b,mult(mult(c,a),b))))]]) ).
cnf(refute_0_98,plain,
$false,
inference(resolve,[$cnf( $equal(mult(a,mult(b,mult(mult(c,a),b))),mult(a,mult(b,mult(mult(c,a),b)))) )],[refute_0_97,refute_0_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP669-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 09:58:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.51/0.73 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.51/0.73
% 0.51/0.73 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.57/0.75
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